Magnetic-Field-Compatible Superconducting Transmon Qubit

We present a hybrid semiconductor-based superconducting qubit device that remains coherent at magnetic fields up to 1 T. The qubit transition frequency exhibits periodic oscillations with the magnetic field, consistent with interference effects due to the magnetic flux threading the cross section of the proximitized semiconductor nanowire junction. As the induced superconductivity revives, additional coherent modes emerge at high magnetic fields, which we attribute to the interaction of the qubit and low-energy Andreev states.

Figure 1

The magnetic-field-compatible device. (a) A micrograph of the transmon qubit island capacitively coupled to a $\lambda /2$ cavity for readout and microwave control. The ground planes and inner conductors of the island and resonator are patterned with a large density of flux-pinning holes for compatibility with large magnetic fields. A nanowire is placed to the right of the island (red rectangle). (b) A scanning electron micrograph of the nanowire and the bottom gates. One side of the wire junction is connected to the island and the other side is connected to the ground plane. (c) A schematic of the device, showing an $\mathrm{In}\mathrm{As}$ nanowire (brown) with one side covered in aluminum (blue) placed on top of two plunger gates ($V_{\mathrm{lplg}}$ and $V_{\mathrm{rplg}}$) that tune the chemical potential in sections (green) of the proximitized $\mathrm{In}\mathrm{As}$. A small region of the superconductor between these two segments is removed to create a Josephson junction, controlled by $V_{\mathrm{cut}}$. A magnetic field, $B$, is applied along the wire axis.

Figure 2

Two-tone spectroscopy as a function of the magnetic field $B$ at $V_{\mathrm{cut}}=-0.5$ V and $V_{\mathrm{lplg}}=V_{\mathrm{rplg}}=-4.2$ V. A variable drive tone, $f_d$, is applied and immediately followed by a readout tone at the cavity resonance frequency, allowing readout of the demodulated transmission voltage, $V_H$. The qubit drive power is adjusted between traces to account for varying lifetime and detuning from the readout cavity, which may cause changes in the background signal and line widths of transitions. Data around $0.58$ T are omitted due to the applied signal power being too low during the two-tone spectroscopy. A line average is subtracted from the data for each $B$. The inset is a sketch illustrating the cross section of a two-facet nanowire, with the hypothesis that the electron density accumulates at the $\mathrm{In}\mathrm{As}$ surface, as illustrated by the color gradient (green to white). A superconducting ring is created by the superconducting $\mathrm{Al}$ shell (blue) and the proximitized $\mathrm{In}\mathrm{As}$ (green). For an axial magnetic field, $B$, a flux, $\mathrm{\Phi }$, threads the nanowire cross section, resulting in a periodic modulation of the qubit frequency. The top horizontal axis is constructed by inferring that a half-integer number of flux quanta, ${\mathrm{\Phi }}_0(=h/2e)$, thread the nanowire at $B=225$ mT.

Figure 3

Time-domain measurements as a function of $B$ at $V_{\mathrm{cut}}=-0.5$ V and $V_{\mathrm{lplg}}=V_{\mathrm{rplg}}=-4.2$ V. (a) Rabi oscillations of the gatemon at $B=0$ and $B=50$ mT. We measure the demodulated transmission, $V_H$, as a function of drive duration, $t$, applied at the qubit frequency. The fits are exponentially damped sinusoids. The data are normalized to the extracted fit parameters. (b) The $T_1$-lifetime measurement at $B=0$ and $B=50$ mT. We measure $V_H$ as a function of the delay time, $\tau$, between the drive and readout tones. To excite the qubit, we apply a $\pi$ pulse calibrated from (a) at $f_q=4.2$ GHz (green) and $f_q=4.1$ GHz (blue). The data are fitted to a decaying exponent to extract $T_1$. (c) [(d)] The same as (a) [(b)] at $B=1$ T with $f_q=2.4$ GHz.

Figure 4

The junction states as a function of the magnetic field and gate. (a) Two-tone spectroscopy for varying $f_d$ and $B$ reveals the oscillating behavior of the junction states at gate voltages $V_{\mathrm{cut}}=-1.8$ V and $V_{\mathrm{lplg}}=V_{\mathrm{rplg}}=-2.0$ V. We observe an uninterrupted qubit transition frequency $f_q$ (arrow) decaying as $B$ increases with multiple new transitions emerging and exhibiting multiple avoided crossings with the qubit transition. (b) Two-tone spectroscopy as a function of $f_d$ and $V_{\mathrm{cut}}$ at $B=350$ mT [left, black rectangle in (a)] and $360$ mT [right, blue rectangle in (a)]. Again, a clear qubit transition is visible, weakly dependent on $V_{\mathrm{cut}}$ with two strongly dispersing transitions coupling to the qubit. The gate-independent transition at $f_d\sim 3.8$ GHz is the qubit transition of the second qubit. A line average is subtracted from each column in all panels.

Figure 5

The transmission voltage, $S_{21}$, as a function of the cavity drive frequency and $B$ showing the field modulation of the resonance frequency of the $\lambda /2$ cavity used for readout in Fig. 2. Due to the large fluctuations, the readout frequency is adjusted each time the magnetic field is varied. The large jumps around $B=0.2$ T are due to corrections of the out-of-plane magnetic field approximately $0.1$ mT (not shown). At $B\sim 150$ mT, the avoided crossing between the resonator and the second qubit is observed.

Figure 6

A schematic of the experimental setup used for the experiments presented. The readout resonator is driven either by the VNA or an arbitrary waveform generator (AWG)-modulated rf source (green lines). The output signal (red lines) is amplified and read out either with the VNA or down-converted by mixing with a reference signal. All microwave equipment is synchronized with a 10-MHz clock reference. Three dc lines (blue) are connected to the three gates, $V_{\mathrm{lplg}}$, $V_{\mathrm{rplg}}$, and $V_{\mathrm{cut}}$, to tune the nanowire chemical potential and junction, respectively.